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Inconsistency coefficient

`Y = inconsistent(Z)`

`Y = inconsistent(Z,d)`

returns the inconsistency coefficient for each link of the hierarchical cluster tree
`Y`

= inconsistent(`Z`

)`Z`

generated by the `linkage`

function. `inconsistent`

calculates the
inconsistency coefficient for each link by comparing its height with the average
height of other links at the same level of the hierarchy. The larger the
coefficient, the greater the difference between the objects connected by the link.
For more information, see Algorithms.

For each link *k*, the inconsistency coefficient is calculated as

$$Y(k,4)=(Z(k,3)-Y(k,1))/Y(k,2),$$

where `Y`

is the inconsistency coefficient
information for links in the hierarchical cluster tree `Z`

.

For links that have no further links below them, the inconsistency coefficient is set to 0.

[1] Jain, A., and R. Dubes. *Algorithms for Clustering
Data*. Upper Saddle River, NJ: Prentice-Hall, 1988.

[2] Zahn, C. T. “Graph-theoretical methods for detecting
and describing Gestalt clusters.” *IEEE Transactions on
Computers*. Vol. C-20, Issue 1, 1971, pp. 68–86.